4. Quadratic Equations Mathematics Exercise - 4.3 class 10 Maths in English - CBSE Study
NCERT Solutions for Class 10 Mathematics are carefully prepared according to the latest CBSE syllabus and NCERT textbooks to help students understand every concept clearly. These solutions cover all important 4. Quadratic Equations with detailed explanations and step-by-step answers for better exam preparation. Each Exercise 4.3 is explained in simple language so that students can easily grasp the fundamentals and improve their academic performance. The study material is designed to support daily homework, revision practice, and final exam preparation for Class 10 students. With accurate answers, concept clarity, and structured content, these NCERT solutions help learners build confidence and score higher marks in their examinations. Whether you are revising a specific topic or preparing an entire chapter, this resource provides reliable and syllabus-based guidance for complete success in Mathematics.
Class 10 English Medium Mathematics All Chapters:
4. Quadratic Equations
3. Exercise 4.3
Exercise: 4.3
Q1. Find the roots of the following quadratic equations, if they exist, by the method of completing the square:
(i) 2x2 - 7x + 3 = 0
Solution: a = 2, b = -7, c = 3Now checking for nature of roots,
D = b2 - 4ac
D = (-7)2 - 4 x 2 x 3
D = 49 - 24
D = 25
Hence D > 0
∴ There is two different and real roots
2x2 - 7x + 3 = 0
Dividing by a term 2 we get.
Putting A term and B term into a2-2ab+b2
(ii) 2x2 + x - 4 = 0;
Solution:
a = 2, b = 1, c = -4
Now checking for nature of roots,
D = b2 - 4ac
D = (1)2 - 4 x 2 x -4
D = 1 - (-32)
D = 1 + 32
D = 33
Hence D > 0
∴ There are two distinct and real roots
2x2 + x - 4 = 0
(iii) 4x2 + 4√3x + 3 = 0
Solution:
a =4, b = 4√3, c= 3
D = b2 - 4ac = (4√3)2 - 4 x 4 x 3
= 48 - 48 = 0
Here D = 0
Therefore, There are two real and equal roots.
4x2 + 4√3x + 3 = 0
⇒(2x)2 + 2 . 2x. √3 + (√3)2 = 0
⇒(2x + √3)2= 0
⇒ (2x + √3) (2x + √3) = 0
⇒ 2x + √3 = 0, 2x + √3 = 0
⇒ 2x = - √3, 2x = - √3
⇒ x = √3/2, x = √3/2
(iv) 2x2 + x + 4 = 0;
a = 2, b = 1, c = 4Now checking for nature of roots,
D = b2 - 4ac
D = (1)2 - 4 x 2 x 4
D = 1 - 32
D = -31
Hence D < 0
∴ There is no real root.
∴ Solution cannot be made of 2x2 + 1x + 4 = 0
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